Finite Group Databasebeta

← #21461773

Subgroups — #21461773

Order 7808.

278 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊M16C211yesmaximal, characteristic
2C2×#14519848C211yesmaximal, characteristic, complemented
3C2×#14519847C211yesmaximal, characteristic, complemented
4#16840733C211yesmaximal, characteristic
5#16840638C211yesmaximal, characteristic, complemented
6#16840638C211yesmaximal, characteristic, complemented
7C22⋊C8×D61C211yesmaximal, characteristic
8C2×#11758213C2211yescharacteristic
9C2×#11758213C2211yescharacteristic
10C2×#11758213C2211yescharacteristic
11C2×#11758213C2211yescharacteristic
12D61⋊M16—22no—
13D61⋊M16—22no—
14C2×#11758217—21no—
15C2×D61⋊C8—21no—
16#14519848—22no—
17#14519847—22no—
18#14519834—21no—
19C22⋊#92420—21no—
20C22×C4×D61C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22C2×C8×D61C2211yescharacteristic
23C22⋊#92418C411yescharacteristic
24#14519689C411yescharacteristic
25#14519689C411yescharacteristic
26C22⋊C8×C61C411yescharacteristic
27C23×D61Q811yescharacteristic
28C22×C4×C61C2×C411yescharacteristic
29C22×Dic61D411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×C4×D61—21no—
34C2×C4×D61C2×C411yescharacteristic
35C2×C4×D61D411yescharacteristic
36C2×C4×D61Q811yescharacteristic
37C2×C4×D61C2311yescharacteristic
38#11758217—24no—
39C2×#92420—21no—
40C2×#92420—21no—
41C2×#92420—21no—
42C2×#92420—21no—
43#11758213—21no—
44#11758213—21no—
45#11758213—21no—
46#11758213—21no—
47#11758213—21no—
48#11758213—21no—
49#11758213D412yes—
50#11758213D412yes—
51D61⋊C8—24no—
52C2×C8×C61C2×C411yescharacteristic
53C2×C8×C61C2×C411yescharacteristic
54C2×#92418C2×C411yescharacteristic
55C2×#92418C2×C411yescharacteristic
56C8×D61—21no—
57C8×D61—21no—
58C8×D61—21no—
59C8×D61—21no—
60C23×C61C4⋊C411yescharacteristic
61C22×D61—22no—
62C22×D61—21no—
63C22×D61—21no—
64C22×D61—41no—
65C22×D61C4⋊C411yescharacteristic
66C22×D61C2×Q811yescharacteristic
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61C4⋊C411yescharacteristic
70C2×C4×C61C22×C411yescharacteristic
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61C4⋊C411yescharacteristic
74C2×Dic61C2×D411yescharacteristic
75C4×D61—21no—
76C4×D61—21no—
77C4×D61—21no—
78C4×D61—21no—
79C4×D61—21no—
80C4×D61—21no—
81C4×D61C2×D411yescharacteristic
82C4×D61C2×D411yescharacteristic
83C4×D61#4111yescharacteristic
84C4×D61#4111yescharacteristic
85#92420—22no—
86#92420—22no—
87#92420—41no—
88#92420—41no—
89C8×C61—21no—
90C8×C61—21no—
91#92418—21no—
92#92418—21no—
93C22×C61—21no—
94C22×C61—21no—
95C22×C61—21no—
96C22×C61C2×C4⋊C411yescharacteristic
97C2×D61—21no—
98C2×D61—21no—
99C2×D61—21no—
100C2×D61—21no—
101C2×D61—42no—
102C2×D61—42no—
103C2×D61#10812yescomplemented
104C2×D61C22⋊Q811yescharacteristic
105C2×D61C22⋊Q811yescharacteristic
106C4×C61—21no—
107C4×C61C4×D411yescharacteristic
108C4×C61C4×D411yescharacteristic
109Dic61—21no—
110Dic61#12011yescharacteristic
111Dic61#12311yescharacteristic
112#1855—611nomaximal, Sylow
113C2×C61—41no—
114C2×C61#38511yescharacteristic
115C2×C61C2×#10811yescharacteristic
116C2×C61#43011yescharacteristic
117D61—22no—
118D61—21no—
119D61—21no—
120C22×M16—611no—
121C2×#108—611no—
122C2×#108—611no—
123#407—611no—
124C2×C22⋊C8—611no—
125#341—611no—
126#341—611no—
127C61#185511yescharacteristic, complemented, Sylow
128C23×C4—611no—
129C2×M16—611no—
130C2×M16—611no—
131C2×M16—611no—
132C2×M16—611no—
133C2×M16—1222no—
134C2×M16—1222no—
135C2×M16—1221no—
136C22×C8—611no—
137C22×C8—611no—
138C22×C8—1221no—
139#108—1222no—
140#108—1222no—
141C22⋊C8—611no—
142C22⋊C8—611no—
143C22⋊C8—611no—
144C22⋊C8—1221no—
145C22⋊C8—1221no—
146C22⋊C8#692311yescharacteristic
147C24—611no—
148C22×C4—611no—
149C22×C4—611no—
150C22×C4—611no—
151C22×C4—611no—
152C22×C4—611no—
153C22×C4—1221no—
154C22×C4—1221no—
155C22×C4—1221no—
156C22×C4—1221no—
157C22×C4C2×#692311yescharacteristic
158M16—612no—
159M16—612no—
160M16—1221no—
161M16—1221no—
162M16—1224no—
163M16—1221no—
164M16—1221no—
165M16—1221no—
166M16—1221no—
167C2×C8—611no—
168C2×C8—611no—
169C2×C8—1221no—
170C2×C8—1221no—
171C2×C8—1221no—
172C2×C8—1221no—
173C2×C8—1221no—
174C2×C8—1221no—
175C2×C8—1224no—
176C2×C8—1221no—
177C2×C8—1221no—
178C2×C8C2×#692311yescharacteristic
179C2×C8C2×#692311yescharacteristic
180C23—611no—
181C23—611no—
182C23—1221no—
183C23—1221no—
184C23—1222no—
185C23—2441no—
186C23C4⋊#692311yescharacteristic
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—611no—
190C2×C4—611no—
191C2×C4—611no—
192C2×C4—611no—
193C2×C4—611no—
194C2×C4—611no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4C4⋊#692311yescharacteristic
204C2×C4C22×#692311yescharacteristic
205C8—21no—
206C8—21no—
207C8—1222no—
208C8—1222no—
209C8—1221no—
210C8—1221no—
211C8—2441no—
212C8—2441no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—611no—
217C22—611no—
218C22—612no—
219C22—1221no—
220C22—1221no—
221C22—1221no—
222C22—1221no—
223C22—2442no—
224C22—2442no—
225C22C2×C4⋊#692311yescharacteristic
226C4—21no—
227C4—611no—
228C4—611no—
229C4—1221no—
230C4D4×#692311yescharacteristic
231C4D4×#692311yescharacteristic
232C2—41no—
233C2—1221no—
234C2—1221no—
235C2—1222no—
236C2#1684070911yescharacteristic
237C2D61⋊#10811yescharacteristic
238C2#1684077711yescharacteristic
subgroupG/H
centerC22C2×C4⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊C8×C61C4
socleC22×C61C2×C4⋊C4
hypercenterC22⋊C8#6923
hypocenterC61#1855
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#14519848C2semidirect
3. C2×#14519847C2semidirect
5. #16840638C2semidirect
6. #16840638C2semidirect
103. C2×D61#108semidirect
127. C61#1855semidirect